What is the electric potential at the point on the axis which is at x = 3.60 m. The length of the rod is L = 1.10 m and the charge on the rod is Q = 5.80 nC

The electric potential V due to a uniformly charged rod at a point along the axis of the rod is given by the formula:

V = kQ * ln[(x+sqrt(x^2+L^2))/L]

where:

• k is Coulomb's constant (8.99 * 10^9 N m^2/C^2),
• Q is the total charge on the rod,
• x is the distance from the end of the rod to the point in question,
• L is the length of the rod.

Given that Q = 5.80 nC = 5.80 * 10^-9 C, L = 1.10 m, and x = 3.60 m, we can substitute these values into the formula to find the electric potential at the point on the axis which is at x = 3.60 m.

V = (8.99 * 10^9 N m^2/C^2) * (5.80 * 10^-9 C) * ln[(3.60 m + sqrt((3.60 m)^2 + (1.10 m)^2))/(1.10 m)]

Now, calculate the value inside the square root:

sqrt((3.60 m)^2 + (1.10 m)^2) = sqrt(12.96 m^2 + 1.21 m^2) = sqrt(14.17 m^2) = 3.77 m

Substitute this back into the formula:

V = (8.99 * 10^9 N m^2/C^2) * (5.80 * 10^-9 C) * ln[(3.60 m + 3.77 m)/(1.10 m)] V = (8.99 * 10^9 N m^2/C^2) * (5.80 * 10^-9 C) * ln[7.37 m/1.10 m] V = (8.99 * 10^9 N m^2/C^2) * (5.80 * 10^-9 C) * ln[6.70]

Finally, calculate the natural logarithm and multiply all the values together to get the electric potential V.